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This lecture delves into distribution functions within the electron theory of advanced metallurgy, explaining how particles distribute on energy levels. It covers the probability of finding particles in different energy states, the concept of degeneracy, and the density of states. The instructor also discusses the differences between Maxwell-Boltzmann and Fermi-Dirac statistics in terms of occupation probability, highlighting the impact of temperature on energy transitions. The lecture concludes by emphasizing how using Maxwell-Boltzmann statistics can overestimate the heat capacity of electrons compared to Fermi-Dirac statistics.